project vs push up

project is a noun but push up is not a noun.

Word	Noun	Adjective	Verb	Adverb
project	Yes	No	Yes	No
push up	No	No	Yes	No

As verbs, push up is a hyponym of project; that is, push up is a word with a more specific, narrower meaning than project:

Other hyponyms of project include overhang, thrust, spear, spear up, bag, bulge, cantilever.

project (noun)	push up (noun)
any piece of work that is undertaken or attempted
a planned undertaking

project (verb)	push up (verb)
present for consideration, examination, criticism, etc.	push upward
regard as objective	push from beneath
communicate vividly	push violently in a specified direction
throw, send, or cast forward
transfer (ideas or principles) from one domain into another
imagine; conceive of; see in one's mind
make or work out a plan for; devise
put or send forth
draw a projection of
cause to be heard
project on a screen
extend out or project in space